Patients with primary biliary cirrhosis will take part in this research study which will test the medications Ursodeoxycholic acid (UDCA) and methotrexate (MTX) for their effects on the illness. Primary biliary cirrhosis (PBC) is a disease of unknown cause in which the small bile ducts of the liver are destroyed slowly by inflammation. Most physicians believe that PBC is due to an abnormal immune response directed against the bile ducts in the liver. It is considered to be an auto-immune disease. Loss of bile ducts causes bile to back up in the liver and ultimately leads to liver damage, liver cirrhosis, and possibly liver failure. Recent information suggests that UDCA and MTX may be useful in the treatment of this disease. The present study will examine whether treatment with UDCA and MTX is better than treatment with UDCA alone. PBC is a chronic disease that tends to progress slowly. In order to meaningfully assess the effectiveness of any treatment, it will probably be necessary to carry on treatment for many years.